Weight average molar mass definition

A normal polymer sample contains molecules with a variety of lengths and it is only possible to quote an average value of the molar mass. A typical distribution of molar mass is shown in Fig. 1.3. Often the exact form of the distribution is not known and it is conventional to describe it in terms of either a number average molar mass, M or a weight average molar mass, My. Both of these parameters can be measured experimentally. In the definition of M and M , it is envisaged that the distribution of molar mass... 

For conversions lower than xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, Mw, respectively. Mn is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. Mw is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

Let s denote with D(x) the ratio between the weight-average and the number-average molar mass in fraction x. Using the definitions, D(x) becomes ... 

In a solution containing both unimer and micelles, Ma, which is by definition more sensitive to low molar mass particles, is always less than the weight-average molecular weight, Mv. Further details on osmometry can be found in the review by Adams (1989), whilst examples of its application to micellar block copolymer solutions are given in Chapter 3. 

The experimental dependence M = /(V), i.e. the classical SEC calibration curve usually obtained by using narrow standards, in such a case can be obtained directly without calibration from the on-line LS detector. By combining the experimental function M = /(V) and the concentration profile (from DRI), one can construct the complete MMD of the HA sample. The differential and cumulative MMD of a high molar mass HA sample (Mw = 652 kDa, D = 2.1) are shown in Fig. (10). Starting from the initial MMD, the molecular weight averages and dispersity index (Mn, Mw, Mz, and D) could be easily calculated using the appropriate definitions. 

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